Question

[lu nguyễn]

tính đạo hàm

a, y= \(\left(2x+3\right)^{21}\left(x-4\right)^{23}\)

b, y= \(\frac{1}{x\sqrt{x}}\)

c, y= \(\sqrt{\frac{x^2+1}{x}}\)

d, y= \(x^2+x\sqrt{x}+1\)

e,y=\(\frac{1+x}{\sqrt{1-x}}\)

f, y= \(\frac{x}{\sqrt{a^2-x^2}}\)

Answer 1

[Nguyễn Việt Lâm]

a/ \(y'=42\left(2x+3\right)^{20}\left(x-4\right)^{23}+23\left(x-4\right)^{22}\left(2x+3\right)^{21}\)

b/ \(y=\frac{1}{x\sqrt{x}}=\frac{1}{\sqrt{x^3}}=x^{-\frac{3}{2}}\Rightarrow y'=-\frac{3}{2}x^{-\frac{5}{2}}=-\frac{3}{2x^2\sqrt{x}}\)

c/ \(y'=\frac{\left(x+\frac{1}{x}\right)'}{2\sqrt{\frac{x^2+1}{x}}}=\frac{1-\frac{1}{x^2}}{2\sqrt{\frac{x^2+1}{x}}}=\frac{\left(x^2-1\right)\sqrt{x}}{2x^2\sqrt{x^2+1}}\)

d/ \(y=x^2+x^{\frac{3}{2}}+1\Rightarrow y'=2x+\frac{3}{2}x^{\frac{1}{2}}=2x+\frac{3}{2}\sqrt{x}\)

e/ \(y'=\frac{\sqrt{1-x}+\frac{1+x}{2\sqrt{1-x}}}{1-x}=\frac{3-x}{2\left(1-x\right)\sqrt{1-x}}\)

f/ \(y'=\frac{\sqrt{a^2-x^2}+\frac{x^2}{\sqrt{a^2-x^2}}}{a^2-x^2}=\frac{a^2}{a^2-x^2}\)